X OF MATHEMATICS
*space-time* of one reference system with respect to any other.
Thus the problem of finding the mathematical expressions for
the intrinsic laws of nature is replaced hy an attackable one in
the theory of invariants. More will be said on this when we come
to Riemann.
In 1863 Cambridge University established a new professor-
ship of mathematics (the Sadlerian) and offered the post to
Cayley, who promptly accepted. The same year, at the age of
forty-two, he married Susan Moline. Although he made less
money as a professor of mathematics than he had at the law,
Cayley did not regret the change. Some years later the affairs
of the University were reorganized and Cayley's salary was
raised. His duties also were increased from one course of lectures
during one term to two* His life was now devoted almost
entirely to mathematical research and university administra-
tion. In the latter his sound business training, even temper,
impersonal judgement, and legal experience proved invaluable.
He never had a great deal to say, but what he said was usually
accepted as final, for he never gave an opinion without having
reasoned the matter through. His marriage and home life were
happy; he had two children5 a son and a daughter. As he
gradually aged his mind remained as vigorous as ever and his
nature became, if anything, gentler. No harsh judgement
uttered in his presence was allowed to pass without a quiet
protest. To younger men and beginners in mathematical careers
he was always generous with his help, encouragement, and
sound advice,
During his professorship the higher education of women was
a hotly contested issue. Cayley threw all his quiet, persuasive
influence on the side of civilization and largely through his
efforts women were at last admitted as students (in their own
nunneries of course) to the monkish seclusion of medieval
Cambridge.
While Cayley was serenely mathematicizing at Cambridge
his friend Sylvester was still fighting the world. Sylvester never
married* In 1854r, at the age of forty, he applied for the profes-
sorship of mathematics at the Royal Military Academy, Wool-
wich. He did not get it. Nor did he get another position for
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